Channel estimation for a very large-scale multiple-input multiple-output (MIMO) system

ABSTRACT

A transmitter, receiver, and method for channel estimation for a Multiple-Input Multiple-Output (MIMO) communication system in which the transmitter includes a multiplicity of transmit antennas spaced such that spacing between adjacent antennas provides a spatial correlation coefficient greater than a threshold level. The transmitter selects a subset of the multiplicity of transmit antennas for transmitting the pilot reference signals. The pilot reference signals are transmitted only from the selected subset of transmit antennas to the receiver. The receiver includes a channel estimator configured to derive a channel estimation for all of the multiplicity of transmit antennas using the received pilot reference signals and known or estimated spatial correlation among the multiplicity of transmit antennas.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of co-pending U.S. patent applicationSer. No. 13/342,688 filed on Jan. 3, 2012, which claims the benefit ofU.S. Provisional Application No. 61/484,047 filed May 9, 2011, thedisclosures of which are fully incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not Applicable

REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTINGCOMPACT DISC APPENDIX

Not Applicable

BACKGROUND

The present invention relates to wireless communication systems. Moreparticularly, and not by way of limitation, the present invention isdirected to a transmitter, receiver, and method for channel estimationfor a Multiple-Input Multiple-Output (MIMO) communication system.

Recent advances in wireless communications have caused a revolution inthe Internet by extending broadband coverage to wireless users. Table 1below is a classification of past, present, and future cellulartechnologies. It is seen that wireless cellular technologies haveprogressively and systematically raised their performance levels by anorder of magnitude over previous generations. Spectral efficiency anddata rate are key metrics that have improved. Some of this improvementhas come about due to increases in the allocated spectrum, while otherimprovements are the result of technological advances, the mostimportant of which have been the introduction of flexible and adaptivechannel coding and modulation, dynamic link adaptation to choose thebest data rate for the radio channel conditions, and the introduction ofMultiple-Input Multiple-Output (MIMO) systems that utilize multipleantennas at the transmitter and or receiver to improve the number ofdegrees of freedom available to reach the users (or to receive fromthem). Similar advances have also been made by standards developed bythe Institute of Electrical and Electronics Engineers (IEEE) within theWireless Local Area Network (WLAN) standard IEEE 802.11, as furtherdeveloped by the WiFi alliance.

TABLE 1 ITU-R Classification — IMT-2000 IMT-Advanced 1G 2G 3G 4GAMPS/NMT GSM/EDGE GSM/WCDMA/ 3GPP LTE Rel. EIA/TIA-136 HSPA/EDGE 10EIA/TIA-95 CDMA2000/evDO 3GPP LTE Rel. 8 Analog Digital Digital Digital<100 KHz <1 MHz <10 MHz <100 MHz 400-1000 MHz 400-2000 MHz 400-3000 MHz200-5000 MHz <10 kb/s/user <1 Mb/s/cell <100 Mb/s/cell <1 Gb/s/cellVoice Voice/data Voice/data Data (voice telephony included) 1985-19991992-present 2002-present 2009-present

MIMO antenna systems increase the throughput of a wireless communicationlink without bandwidth expansion. Through proper design of thesignal-transmission scheme and the corresponding receiver algorithm, theMIMO channel may be decomposed into parallel non-interfering channels.The number of such parallel channels, or streams, is the smaller of thenumber of transmit antennas and the number of receive antennas. When allthe receive antennas are attached to the same User Equipment (UE), thesystem is referred to as Single-User MIMO (SU-MIMO). When the receiveantennas are distributed among multiple UEs, the system is referred toas Multi-User MIMO (MU-MIMO). Because of its great potential inbandwidth efficiency, MIMO has been adopted by most wirelesscommunication standards such as Long Term Evolution (LTE), WiMax, andWiFi.

In order to exploit the potential of the MIMO channel, it is critical tohave knowledge of the MIMO channel state information. This informationis needed for the receiver to perform the demodulation of transmitteddata symbols. It is also needed sometimes at the transmitter to properlyshape the transmit signal to improve Signal to Interference and NoiseRatio (SINR) at the receiver.

In a wireless communication system employing Orthogonal FrequencyDivision Multiplexing (OFDM), the channel state information can bemodeled as a slowly varying, 2-dimensional, complex time-frequencyprocess. Known Reference Signals (RS), i.e, pilot symbols, aretransmitted at various time instants and frequencies.

FIG. 1 illustrates a pilot RS for MIMO in an LTE system. When the RSsare properly distributed across the time-frequency plane, the receivercan use these known symbols to reconstruct the full channel response.Naturally, the density of the pilots depends on the rate at which thechannel varies in time and frequency. For LTE employing two transmitantennas, the pilots are transmitted at a higher density, as shown inFIG. 1. For four transmit antennas, the last two antennas have lowerpilot density since it is anticipated that the channel variation isslower for the scenarios that can exploit four antennas.

Since the antennas are co-located, the transmit signals interfereseverely with each other. In order for the receiver to receive thepilots without interference, an antenna mutes its transmission at thelocations where pilots are transmitted by other antennas, as marked bythe shaded areas. In total, 24 resource elements out of every 168 arereserved overhead for pilot transmission in LTE.

Recently, there have been growing interests in extending the MIMO systemto a very large number of transmit and receive antennas. Instead of fourto eight antennas typically employed in current systems, the number ofantennas envisaged in these recent studies ranges in the order of 100 ormore. Supported by the random matrix theory, it has been suggested thatthe required energy per bit vanishes as the number of antennas goes toinfinity.

SUMMARY

Even if the theory holds for an arbitrarily large number of antennas andthat the hardware can support the construction of such a large array inpractice, the number of transmit antennas will still be limited by theoverhead their pilot symbols occupy. Using LTE as an example, if 24 outof 168 resource elements are required to support four transmit antennas,then the largest number of antennas the LTE system can support is 28. Atthat level, however, there will be no resource element left for datatransmission.

The present invention provides a solution to the above-mentionedproblems. In exemplary embodiments of the invention, only a subset of amultiplicity of antennas transmits pilot symbols, and then the spatialcorrelation among closely placed antennas is exploited to derive thechannel estimation for all antennas. This spatial correlation may beestimated or may be known a priori. A Minimum Mean Square Estimator(MMSE), for example, may be used to interpolate the channel for antennasthat do not transmit pilot symbols.

In one embodiment, the present invention is directed to a method oftransmitting pilot reference signals utilized by a receiver for channelestimation in a MIMO communication system in which a transmitterutilizes a plurality of transmit antennas. The method includes the stepsof spacing the plurality of transmit antennas such that spacing betweenadjacent antennas provides a spatial correlation coefficient greaterthan a threshold level; selecting by the transmitter, a selected subsetof the plurality of transmit antennas for transmitting the pilotreference signals; and transmitting the pilot reference signals onlyfrom the selected subset of transmit antennas to a receiver.

In another embodiment, the present invention is directed to a method ofchannel estimation for a MIMO communication system in which atransmitter utilizes a plurality of transmit antennas. The methodincludes the steps of receiving by a receiver, pilot reference signalstransmitted only from a selected subset of the plurality of transmitantennas; and deriving a channel estimation for all of the plurality oftransmit antennas using spatial correlation among the plurality oftransmit antennas.

In another embodiment, the invention is directed to a transmitter fortransmitting pilot reference signals utilized by a receiver for channelestimation in a MIMO communication system. The transmitter includes aplurality of transmit antennas spaced such that spacing between adjacentantennas provides a spatial correlation coefficient greater than athreshold level; an antenna subset selector configured to select asubset of the plurality of transmit antennas for transmitting the pilotreference signals; and a radio frequency transmitter coupled to theselected subset of transmit antennas for transmitting the pilotreference signals only from the selected subset of transmit antennas tothe receiver.

In another embodiment, the invention is directed to a receiver in a MIMOcommunication system in which a transmitter utilizes a plurality oftransmit antennas. The receiver includes a radio frequency receiverconfigured to receive pilot reference signals transmitted only from aselected subset of the plurality of transmit antennas; and a channelestimator configured to derive a channel estimation for all of theplurality of transmit antennas using the received pilot referencesignals and known or estimated spatial correlation among the pluralityof transmit antennas.

In another embodiment, the invention is directed to a method oftransmitting pilot reference signals utilized by a receiver for channelestimation in a MIMO communication system in which a transmitterutilizes a plurality of transmit antennas. The method includes the stepsof selecting by the transmitter, a selected subset of the plurality oftransmit antennas for transmitting the pilot reference signals; andtransmitting the pilot reference signals only from the selected subsetof transmit antennas through a propagation environment to a receiver;wherein the selecting step includes selecting transmit antennas at aninterval in the spatial domain depending on scattering characteristicsof the propagation environment such that the receiver can interpolatethe channel over those antennas that do not transmit pilot referencesignals.

An advantage of certain embodiments of the present invention is asignificant reduction of the pilot overhead in a large scale MIMOsystem.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following section, the invention will be described with referenceto exemplary embodiments illustrated in the figures, in which:

FIG. 1 (Prior Art) illustrates a transmission scheme for a pilotReference Signal (RS) for MIMO in an LTE system;

FIG. 2 is an illustrative drawing of an exemplary embodiment of thepresent invention in which pilot symbols are transmitted by only asubset of a plurality of antennas;

FIG. 3 is a graphical representation of a correlation coefficient of alinear antenna array as a function of the distance between a point andthe center of the array;

FIG. 4 is an illustrative drawing of a uniformly spaced linear antennaarray;

FIG. 5 illustrates a transmission scheme for transmitting pilot RSs froma subset of the antennas of FIG. 4 in an exemplary embodiment of thepresent invention;

FIG. 6 illustrates a particular embodiment of the present inventionimplemented in an LTE network;

FIG. 7 is a simplified block diagram of an exemplary User Equipment (UE)for use with the present invention;

FIG. 8 is a simplified block diagram of an exemplary base station 13 foruse with the present invention;

FIG. 9 is a flow chart illustrating the steps of an exemplary embodimentof the method of the present invention; and

FIG. 10 is a simplified block diagram of an exemplary embodiment of thesystem 50 of the present invention.

DETAILED DESCRIPTION

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of the invention.However, it will be understood by those skilled in the art that thepresent invention may be practiced without these specific details. Inother instances, well-known methods, procedures, components and circuitshave not been described in detail so as not to obscure the presentinvention. Additionally, it should be understood that the invention maybe implemented in hardware or in a combination of hardware and softwarein which a processor executes the steps of the invention when executingcomputer program instructions stored on a non-transitory memory.

FIG. 2 is an illustrative drawing of an exemplary embodiment of thepresent invention in which pilot symbols are transmitted by only asubset of a plurality of antennas. The circled antennas illustrate thetransmitting subset. In this embodiment, a processor exploits thespatial correlation among closely placed antennas to derive the channelestimation for all antennas. This spatial correlation may be estimatedor may be known a priori. An estimator such as an MMSE, for example, maybe used to interpolate the channel for antennas that do not transmitpilot symbols.

FIG. 3 is a graphical representation of a correlation coefficient of alinear antenna array as a function of the distance between a point andthe center of the array. It can be seen that the correlation coefficientbecomes zero when the distance is approximately eight times thewavelength. Conversely, the correlation coefficient reaches unity whenthe distance is zero. Thus, if the separation between the antennas inthe array is very small, the correlation is very high, and there is noneed to transmit pilot signals on all of the antennas. A similar effectcan be observed with two-dimensional arrays such as those arranged in arectangular fashion as in FIG. 2, arrays arranged partly or wholly incylindrical fashion, or arrays that may be arranged partly or wholly onthe surface of an imagined sphere. The correlation function is thentwo-dimensional. Thus, the transmit antennas in the subset of transmitantennas may be selected such that spacing between the selected antennasprovides a correlation coefficient greater than a threshold level suchas, for example, 0.9.

FIG. 4 is an illustrative drawing of a uniformly spaced linear antennaarray suitable for implementing an embodiment of the present invention.Extension to two-dimensional or even 3-dimensional arrays with arbitraryspacing is straightforward. Let h₀(t₀,f₀,m₀) be the time-frequencychannel response between transmit antenna m₀ and a certain receiveantenna on a UE sampled at time t₀ and frequency f₀. Then thecorrelation between two such samples may be given by:ρ(t ₀ ,t ₁ ,f ₀ ,f ₁ ,m ₀ ,m ₁)=E{h ₀(t ₀ ,f ₀ ,m ₀)h ₁*(t ₁ ,f ₁ ,m₁)}  (1)

In practice, this correlation is usually a function of the differencesbetween the corresponding variables. In other words,ρ(t ₀ ,t ₁ ,f ₀ ,f ₁ ,m ₀ ,m ₁)={tilde over (ρ)}(t ₀ −t ₁ ,f ₀ −f ₁ ,m ₀−m ₁)  (2)for some function {tilde over (ρ)}. This fact has been widely acceptedin the case of time-frequency channel response. The same is true for thecase of a linear array when the size of the array is much smaller thanthe distance between the transmit and receive antennas.

In any case, the correlation function given in Equation (1) depends onthe scattering environment and usually remains unchanged for a UE for anextended period of time. This is again widely accepted for thetwo-dimensional, time-frequency channel response. Therefore, it can beestimated and known a priori. Such correlation can be exploited in thespatial domain to achieve more efficient channel estimation for a verylarge scale MIMO system.

Transmission

FIG. 5 illustrates a transmission scheme for transmitting pilot RSs froma subset of the antennas of FIG. 4 in an exemplary embodiment of thepresent invention. Instead of transmitting pilots on all antennas,pilots are transmitted only on antennas 0, 4, and 8. These pilot symbolsare marked by R₀, R₄, and R₈, respectively. They occupy orthogonallocations on the time-frequency plane, as in the case of an LTE RS. Asindicated, the spacing between adjacent antenna elements is half awavelength, the correlation between two adjacent elements is very high(>0.9 according to FIG. 3). Therefore, transmitting pilots on every5^(th) antenna is more than adequate as can be easily verified by anywell-designed channel estimator such as the one described below.

Another aspect of the present invention is that pilot signals may betransmitted in the spatial domain (whether 1-D, 2-D, or even 3-D arrays)with a density such that the receiver can interpolate the channel overthose antennas that do not have pilot symbols, rather than spacing theantennas at a certain interval (such as half a wavelength) such that thepilot can be transmitted at a lower density. The pilot should betransmitted at an interval in the spatial domain depending on thescattering characteristics of the propagation environment.

In general, embodiments of the present invention transmit pilot signalsonly on every T_(m,v) antennas in the vertical dimension and everyT_(m,h) antennas in the horizontal dimension to reduce pilot redundancyin a large-scale antenna array, where T_(m,v) is inversely proportionalto the transmit elevation angular spread, and T_(m,h) is inverselyproportional to the transmit azimuth angular spread.

Channel Estimation at the Receiver

Assuming the pilot symbols are all ones, the received signal r_(P0)corresponding to the pilot symbol transmitted by antenna m_(p) ₀ at timet_(p) ₀ and frequency f_(p) ₀ may be given by:r _(p) ₀ (t _(p) ₀ ,f _(p) ₀ ,m _(p) ₀ )=h _(p) ₀ (t _(p) ₀ ,f _(p) ₀ ,m_(p) ₀ )+z _(p) ₀ (t _(p) ₀ ,f _(p) ₀ ,m _(p) ₀ )  (3)where z_(p) ₀ (t_(p) ₀ ,f_(p) ₀ ,m_(p) ₀ ) is the Additive WhiteGaussian Noise (AWGN) with variance σ_(z) ², and h_(p0) is the channelcoefficient at p0, where p0 is a point in the time-frequency-antennaspace at which a pilot signal is transmitted. The pilot signals haveindices p0, p1, p2, . . . to distinguish from other indices at whichdata is transmitted. By arranging all the pilot observations in a columnvector, the following is obtained:

$\begin{matrix}{\begin{bmatrix}r_{p_{0}} \\\vdots \\r_{p_{N}}\end{bmatrix} = {\begin{bmatrix}h_{p_{0}} \\\vdots \\h_{p_{N}}\end{bmatrix} + \begin{bmatrix}z_{p_{0}} \\\vdots \\z_{p_{N}}\end{bmatrix}}} & (4)\end{matrix}$or more concisely,r _(p) =h _(p) +z _(p)  (5)

The channel h₀(t₀,f₀,m₀) at any time t₀, frequency f₀ for any givenantenna m₀ can be estimated using an MMSE channel estimator given by:ĥ ₀ =E{h ₀ h _(p)}(E{h _(p) h _(p)}+σ_(z) ² I)⁻¹ r _(p)  (6)

Since the channel's correlation function is known, Equation (6) can bereadily evaluated. Note that the channel's correlation functionencompasses correlation in all three dimensions of time, frequency, andspace (antenna). For a given time and frequency, the spatial correlationis the same as shown in FIG. 3. While it is known to exploiting theknowledge of correlation in time and frequency for pilot transmissionand channel estimation, embodiments of the present invention exploitcorrelation in the spatial domain, which is heretofore unknown. The twoadditional dimensions of time and frequency are included above forcompleteness.

Note that there are low-complexity suboptimal alternatives to Equation(6). One such alternative is based on the Least Squares estimate.Equation (6) is given as an exemplary method of performing channelestimation for the inventive pilot transmission method.

Once the channel is estimated, the terminal may use it for demodulationof downlink transmissions. The receiver may also feed back the channelinformation to the transmitter for downlink pre-coding (beamforming).For example, the receiver may feed back a compressed version of the MIMOchannel by extracting representative features such as delay-Doppler andangular response.

The present invention may be implemented in any appropriate type oftelecommunication system supporting any suitable communication standardsand using any suitable components.

FIG. 6 illustrates a particular embodiment of the present inventionimplemented in an LTE network. As shown, an example network 11 mayinclude one or more instances of user equipment (UEs) 12 a-12 c and oneor more base stations 13 a-13 c capable of communicating with the UEs,along with any additional elements suitable to support communicationbetween UEs or between a UE and another communication device (such as alandline telephone). The illustrated UEs may represent communicationdevices that include any suitable combination of hardware or combinationof hardware and software.

FIG. 7 is a simplified block diagram of an exemplary UE 12 for use withthe present invention. The example UE may include a processor 21, anon-transitory memory 22, a transceiver 23, and an antenna 24. Inparticular embodiments, some or all of the functionality described aboveas being provided by mobile communication devices or other forms of UEmay be provided by the UE processor 21 executing instructions stored onthe non-transitory memory 22. Alternative embodiments of the UE mayinclude additional components beyond those shown in FIG. 7 that may beresponsible for providing certain aspects of the UE's functionality,including any of the functionality described above and/or anyfunctionality necessary to support the embodiments of the presentinvention described above.

FIG. 8 is a simplified block diagram of an exemplary base station 13 foruse with the present invention. The example base station may include aprocessor 31, a non-transitory memory 32, a transceiver 33, an antenna34, and a network interface 35. In particular embodiments, some or allof the functionality described above as being provided by a mobile basestation, a base station controller, a node B, an enhanced node B, and/orany other type of mobile communications node may be provided by the basestation processor 31 executing instructions stored on the non-transitorymemory 32. Alternative embodiments of the base station may includeadditional components responsible for providing additionalfunctionality, including any of the functionality identified aboveand/or any functionality necessary to support the embodiments of thepresent invention described above.

FIG. 9 is a flow chart illustrating the steps of an exemplary embodimentof the method of the present invention. At step 41, the antennas in aplurality of transmit antennas for a transmitter such as a base stationare spaced so that they have good spatial correlation. A threshold valueof the correlation coefficient may be predefined, and antennas may bespaced to provide a correlation coefficient greater than the thresholdvalue. At step 42, a subset of the transmit antennas is selected, andthe transmitter transmits pilot reference signals only from the selectedsubset of transmit antennas. At step 43, a receiver such as a UEreceiver receives the pilot reference signals transmitted from theselected subset of transmit antennas. At step 44, the receiver obtainsor estimates the spatial correlation coefficient for the selected subsetof transmit antennas.

At step 45, the receiver utilizes an estimator (MMSE, LS, etc.) tointerpolate the channel for the transmit antennas that did not transmitthe pilot reference signals. At step 46, the receiver utilizes thechannel estimate to demodulate downlink transmissions. At step 47, thereceiver may feed back the channel estimate or the compressed MIMOchannel to the transmitter. At step 48, the transmitter may utilize thechannel estimate for downlink pre-coding.

FIG. 10 is a simplified block diagram of an exemplary embodiment of asystem 50 of the present invention. The system may include a transmitter51 and a receiver 52. Within the transmitter, an antenna subset selector53 may receive as inputs or may store internally, knowledge of antennaelement spacing, the relationship between spacing and the correlationcoefficient, and the correlation coefficient threshold. From thisknowledge, the antenna subset selector selects a subset 54 of thetransmit antennas 55 to transmit pilot RSs. A pilot RS transmitter 56then transmits pilot RSs on the selected subset of (circled) transmitantennas.

Within the receiver 52, a pilot RS receiver 57 receives the pilot RSfrom the selected subset of transmit antennas. The receiver obtainsspatial correlation information or utilizes a spatial correlationestimator 58 to estimate the spatial correlation coefficient for theplurality of transmit antennas. The received signal and the spatialcorrelation coefficient are input to a channel estimator such as an MMSEor LS estimator 59, which interpolates the channel for the transmitantennas that did not transmit the pilot RSs. The resulting channelestimate 61 is then provided to a demodulator 62 to demodulate downlinktransmissions.

The receiver 52 may also feed back the channel estimate or thecompressed MIMO channel to the transmitter 51 for use in pre-coding. Inthis event, the resulting channel estimate may be provided to a channelestimate transmitter 63, which transmits the channel estimate to thetransmitter. Within the transmitter, the channel estimate is receivedand provided to a pre-coder 64 to assist with downlink pre-coding.

As will be recognized by those skilled in the art, the innovativeconcepts described in the present application can be modified and variedover a wide range of applications. Accordingly, the scope of patentedsubject matter should not be limited to any of the specific exemplaryteachings discussed above, but is instead defined by the followingclaims.

What is claimed is:
 1. A method of transmitting pilot reference signalsutilized by a receiver for channel estimation in a Multiple-InputMultiple-Output (MIMO) communication system in which a transmitterutilizes a plurality of transmit antennas, the method comprising thesteps of: spacing the plurality of transmit antennas such that spacingbetween adjacent antennas provides a spatial correlation coefficientgreater than a threshold level; selecting by the transmitter, a selectedsubset of the plurality of transmit antennas for transmitting the pilotreference signals; and transmitting the pilot reference signals onlyfrom the selected subset of transmit antennas through a propagationenvironment to a receiver; wherein the selecting step includes selectingtransmit antennas at an interval in the spatial domain depending onscattering characteristics of the propagation environment, wherein theinterval between selected transmit antennas is greater than adjacentantennas, but still provides a density of transmitted pilot signalssufficient to enable the receiver to interpolate the channel over thoseantennas that do not transmit pilot reference signals.
 2. The method asrecited in claim 1, wherein the plurality of transmit antennas isarranged in an array having a vertical dimension and a horizontaldimension, and the selecting step reduces redundancy of the pilotreference signals in the array by: selecting every T_(m,v) antennas inthe vertical dimension; and selecting every T_(m,h) antennas in thehorizontal dimension; where T_(m,v) is inversely proportional to atransmit elevation angular spread, and T_(m,h) is inversely proportionalto a transmit azimuth angular spread.
 3. The method as recited in claim1, wherein the spacing between adjacent antennas is equal to or lessthan one-half wavelength of the transmitted pilot reference signals. 4.A transmitter for transmitting pilot reference signals utilized by areceiver for channel estimation in a Multiple-Input Multiple-Output(MIMO) communication system, the transmitter comprising: a plurality oftransmit antennas spaced such that spacing between adjacent antennasprovides a spatial correlation coefficient greater than a thresholdlevel; an antenna subset selector configured to select a subset of theplurality of transmit antennas for transmitting the pilot referencesignals; and a radio frequency transmitter coupled to the selectedsubset of transmit antennas and configured to transmit the pilotreference signals only from the selected subset of transmit antennasthrough a propagation environment to the receiver; wherein the antennasubset selector is configured to select transmit antennas at an intervalin the spatial domain depending on scattering characteristics of thepropagation environment, wherein the interval between selected transmitantennas is greater than adjacent antennas, but still provides a densityof transmitted pilot signals sufficient to enable the receiver tointerpolate the channel over those antennas that do not transmit pilotreference signals.
 5. The transmitter as recited in claim 4, wherein theplurality of transmit antennas is arranged in an array having a verticaldimension and a horizontal dimension, and the selecting step reducesredundancy of the pilot reference signals in the array by: selectingevery T_(m,v) antennas in the vertical dimension; and selecting everyT_(m,h) antennas in the horizontal dimension; where T_(m,v) is inverselyproportional to a transmit elevation angular spread, and T_(m,h) isinversely proportional to a transmit azimuth angular spread.
 6. Thetransmitter as recited in claim 4, wherein the spacing between adjacentantennas is equal to or less than one-half wavelength of the transmittedpilot reference signals.